Calculate the quotient below and give your answer in scientific notation. ${\dfrac{1.20\times 10^{6}}{6.0\times 10^{5}}} =\ ?$
Answer: Start by collecting the significands and exponents. $ {\dfrac {{1.20} \times {10^{6}}} {{6.0} \times {10^{5}}} = {\dfrac{1.20}{6.0}} \times {\dfrac{10^{6}}{10^{5}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.20} \times {10^{6 \,-\, 5}}$ $= {0.20} \times {10^{1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.20}$ is the same as ${2.0 \div 10}$, or ${2.0 \times 10^{-1}}$. $ = {2.0 \times 10^{-1}} \times {10^{1}} $ $ = 2.0 \times 10^{{-1} + {1}} $ $= 2.0\times 10^{0}$